Fractional Tikhonov regularization method in Hilbert scales

作者：

Highlights：

• Fractional Tikhonov regularization (FTR) model for non-linear operator equations is studied.

• The model is analyzed in the setting of Hilbert scales.

• With Holder type source condition, an optimal error estimate is obtained.

• The numerical verification is validated using various examples.

摘要

•Fractional Tikhonov regularization (FTR) model for non-linear operator equations is studied.•The model is analyzed in the setting of Hilbert scales.•With Holder type source condition, an optimal error estimate is obtained.•The numerical verification is validated using various examples.

论文关键词：Ill-posed problem,Fractional Tikhonov regularization,Hilbert scales,Parameter choice strategy

论文评审过程：Received 8 November 2019, Revised 24 August 2020, Accepted 20 September 2020, Available online 10 October 2020, Version of Record 10 October 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125701